Approximate the value of the volume of the solid generated b

Approximate the value of the volume of the solid generated by revolving the region bounded by the graph of the equations about the x - axis. Show the graph of the function and sketch the solid. (use a proper format and scale, work without the required quality will not be accepted)

y=e^x/2 + e^-x/2 , y=0 , x=-1, x=2

Please I need to have this question answered in details!

Thank you very much!

Solution

V = pi * int y^2 dx (-1 < x < 2) =

pi * int (e^x + e^(-x) + 2) dx =

pi * (e^x - e^(-x) + 2x) (-1 < x < 2) =

pi * (e^2 - e^(-2) + 4 - e + e^(-1) + 2) =

pi * (e^2 - 1/e^2 + 6 - e + 1/e)